Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C13×M16 ⋊ C4 |
| Sylow | C13 ⋊ #1729 |
416 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|a^2=e,b^2=f,e^2=g,b^a=bd,h^a=h^5,c^b=cg,h^b=h^8,h^e=h^12,h^f=h^12116 conjugacy classes — view the full character table.
| maximal subgroup of | #16777259, #16777265, #16785368, … |
| maximal normal subgroup of | #16777259, #16777265, #16785368, … |
| maximal quotient of | #16778890, #16778891, #16778898, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20178);